Playing Cards Probability Questions | How to Find the Probability of Playing Cards?

One of the major roles played in the Probability concept in mathematics is a deck of 52 playing cards. The concept of Playing cards probability problems is solved on the basis of a well-shuffled pack of 52 cards. Whenever we face the probability topic in statistics, most of the problems with a well-shuffled pack of 52 playing cards. So, this article will make you learn what is the basic concept of cards, the formula, how to find the probability of playing cards, and worked-out problems on Playing Cards Probability.

Basic Stuff About Playing Cards Probability

In a deck or pack of playing cards, you will find the 52 playing cards which are divided into 4 suits of 13 cards. The shapes of those 4 suits are i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣. Also, these 4 suits are colored in two colors ie., red and black. Spades and clubs are black in color and the remaining Diamonds and hearts are Red in color.

The four different types of cards are shown in the picture given below.

How are 52 Cards Divided?

In each suit of playing cards includes an Ace, King, Queen, Jack or Knaves, 10, 9, 8, 7, 6, 5, 4, 3, and 2. In the pack of 52 cards, there are 12 face cards which are King, Queen, and Jack (or Knaves). Check out the below image and get full clarity about the 13 cards of each suit in the 52 playing cards.

Also, have a look at the below points to memorize easily about the pack of 52 playing cards:

1. Club – 13 cards
2. Heart – 13 cards
3. Spade – 13 cards
4. Diamond – 13 cards
5. No. of black cards – 26
6. No. of red cards – 26
7. No. of Ace cards (named as “A”) – 4
8. No. of Jack cards (named as “J” – 4
9. No. of Queen cards (named as “Q”) – 4
10. No. of King cards (named as “K”) – 4
11. No. of face cards (named as “J”, “Q” and “K”) – 12

Formula

Based on the classic definition of the probability the formula to find the probability with playing cards is as follows:

Probability = No. of favorable comes/ No.of all possible outcomes
          or
P(A) = n(A)/n(S)

In the case of 52 playing cards, n(S) = 52.

How to Find the Probability of Playing Cards?

In the following steps, we have explained how to find the probability of playing cards. So, follow the below steps to calculate the probability:

1. In the first step, you have to find the number of favorable events.
2. Next, identify the whole number of possible outcomes that can occur.
3. At last, divide the number of favorable events by the complete number of possible outcomes.

To help you in solving the playing cards probability, we have given some solved examples of probability below. Let’s get into the practice problems of playing cards probability.

Probability Cards Questions

Example 1:

A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability that the drawn card is Queen?

Solution:

Assume E be the event of drawing a Queen Card.

In total there are 4 Queen cards in 52 playing cards

Then,

n(E) = 4

And, we know that

n(S) = 52

Now, apply the formula to find the playing cards probability for the drawn card,

P(E) = n(E) / n(S)

P(E) = 4/52 = 1/13

So, the probability of getting a Queen card is 1/13.

Example 2:

A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting a card of Heart.

Solution:

Let A represents the event of getting a Heart cart.

No.of Heart cards are 13

Therefore, n(A) = 13

Here, the total no. of possible outcomes of A is 52

P(A) = No.of favourable comes/ a total no. of possible outcomes of A

= n(A)/n(S)

=13/52

=1/4

Hence, the required probability of getting a card of Heart is 1/4.